Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 5 + (x - 2)/3 = (x + 3)/8

Key Concepts

Linear Equations

Linear equations are mathematical statements that express the equality of two linear expressions. They typically take the form ax + b = c, where a, b, and c are constants, and x is the variable. Understanding how to manipulate these equations is essential for finding the value of x that satisfies the equation.

Solving Equations with Fractions

When solving equations that contain fractions, it is often helpful to eliminate the denominators to simplify the equation. This can be achieved by multiplying both sides of the equation by the least common denominator (LCD) of all fractions involved. This step makes it easier to isolate the variable and solve for its value.

Isolating the Variable

Isolating the variable is a fundamental technique in solving equations, where the goal is to get the variable (e.g., x) on one side of the equation and all other terms on the opposite side. This often involves performing inverse operations, such as addition, subtraction, multiplication, or division, to simplify the equation step by step until the variable is alone.